Well, it's an LLC once the human initializers withdraw from it, that's the legal trick here. If you mean what is the actual algorithm using the LLC shell, it could be anything. A simple flowchart, a DAC on Ethereum, a NN on AWS, whatever.
I've sometimes wondered how, or whether, this is guaranteed for companies whose ownership is organised by tradeable shares.
That is, whether there's anything that stops a sequence of share sales ending up in a situation where a set of companies between them own all the shares of companies in the set.
(If this ever happened, presumably the last human to sell a share to one of the companies was making a mistake, but humans make mistakes all the time.)
I mean, normally if you wanted to stop this sort of thing you'd do something like introduce a hierarchy of company types and say type N companies may only own shares in companies of type N+1 or higher. But I've never heard of such a rule.
People get away with illegal or unlawful things all the time because of the unawareness of the authorities, but that doesn't change the nature of those things.